In a vote for student council president, $4$ out of $5$ students voted. If $432$ votes were cast, how many students were in the school? Show steps.

Full solution

Q. In a vote for student council president,

4

out of

5

students voted. If

432

votes were cast, how many students were in the school? Show steps.

Given Information: We know that $4$ out of $5$ students voted, which means the fraction of students who voted is $\frac{4}{5}$ .
Setting up Equation: If $432$ votes were cast, and this represents $\frac{4}{5}$ of the students, we can set up the equation $(\frac{4}{5}) \times \text{total\_students} = 432$ to find the total number of students.
Calculating Total Students: To find the total number of students, we need to divide $432$ by $\frac{4}{5}$ . This is the same as multiplying $432$ by the reciprocal of $\frac{4}{5}$ , which is $\frac{5}{4}$ .
Calculating Total Students: To find the total number of students, we need to divide $432$ by $\frac{4}{5}$ . This is the same as multiplying $432$ by the reciprocal of $\frac{4}{5}$ , which is $\frac{5}{4}$ .Calculate $432 \times \left(\frac{5}{4}\right)$ to get the total number of students. $\newline$ $432 \times \left(\frac{5}{4}\right) = 540$